# Generalized Sparse Additive Model with Unknown Link Function

arXiv: https://arxiv.org/abs/2410.06012 · HTML: https://mlsanity.com/paper/2410.06012/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 8 Oct 2024.

## Builds on (most cited first, 11 of 11)

- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection](https://mlsanity.com/paper/2209.09326/) (2022)
- [Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity](https://mlsanity.com/paper/2202.12482/) (2022)
- [Scalable Interpretability via Polynomials](https://mlsanity.com/paper/2205.14108/) (2022)
- [CMW-Net: Learning a Class-Aware Sample Weighting Mapping for Robust Deep Learning](https://mlsanity.com/paper/2202.05613/) (2022)
- [Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition](https://mlsanity.com/paper/1503.02817/) (2015)
- [Curve Your Enthusiasm: Concurvity Regularization in Differentiable Generalized Additive Models](https://mlsanity.com/paper/2305.11475/) (2023)
- [Generalized Sparse Additive Models](https://mlsanity.com/paper/1903.04641/) (2019)
- [Learning rates for the risk of kernel based quantile regression estimators in additive models](https://mlsanity.com/paper/1405.3379/) (2014)

## Built on by (most cited first, 1 of 1)

- [Quantifying Multimodal Capabilities: Formal Generalization Guarantees in Pairwise Metric Learning](https://mlsanity.com/paper/2605.01424/) (2026)

## Abstract (arXiv)

Generalized additive models (GAM) have been successfully applied to high dimensional data analysis. However, most existing methods cannot simultaneously estimate the link function, the component functions and the variable interaction. To alleviate this problem, we propose a new sparse additive model, named generalized sparse additive model with unknown link function (GSAMUL), in which the component functions are estimated by B-spline basis and the unknown link function is estimated by a multi-layer perceptron (MLP) network. Furthermore, ℓ2,1-norm regularizer is used for variable selection. The proposed GSAMUL can realize both variable selection and hidden interaction. We integrate this estimation into a bilevel optimization problem, where the data is split into training set and validation set. In theory, we provide the guarantees about the convergence of the approximate procedure. In applications, experimental evaluations on both synthetic and real world data sets consistently validate the effectiveness of the proposed approach.